台雪成与合作者在计算数学，特别是在数值分析和图像处理领域，做出了重大贡献。他是 AOS（加算子分裂）算法
的发明者之一，此算法因其快速、稳定和高效，已经成为偏微分方程的图像处理中非常受欢迎的过滤算法。雪成在数值
分析研究方面也做出了具有创新性的一些新算法。他的“障碍问题算法”是至今为止“唯一被证明具有多重网格收敛速
度的算法 ” 。雪成对奇异摄动分析也有很好的工作，在实际工程模拟中已经得到应用 。
    最近，雪成转向图像处理方面的研究。一个利用水平集方法解决反问题的一般框架被提了出来，此方法已经被扩展
到了形状识别和优化等一大类问题。他最近提出了 PCLSM（分段常数水平集方法），以及高阶滤波器和图像处理的新的
几何模型，这些工作得到了国际知名专家的高度评价。另外他还获得了大量的科学研究经费支持，表明他的研究工作在
国际上获得了广泛承认。
     Tai has made significant contributions to computational mathematics especially in the areas related 
to numerical analysis and image processing in collaboration with coworkers. Tai is one of the inventors for 
the AOS (additive operator splitting) scheme which is highly popular for PDE-based image processing since 
it is fast and allow s stable and efficient filtering. Tai's original research on numerical analysis has 
produced several new schemes. The algorithm of Tai on obstacle problems is the “only algorithm with proven 
multigrid convergence rate”. Tai's work on singular perturbation analysis is creative and have been used 
for real engineering simulations.
     Recently, he has shifted his interests to image processing. A general framework of us ing level set  
idea for inverse problems was proposed. This has been extended to a large class of problems related to shape 
identification and optimization.  Tai proposed PCLSM (piecewise constant level set methods) for multiphase 
interface problems, and higher order filters and new geometrical models for image processing. These researches 
have also been highly praised by leading international experts.
     Having been widely cited and having attracted a large amount of external research fund s indicate that
 Tai's research has been highly recognized internationally.